Mathematics Archives - Page 2 of 89 - Student Notes

Predictive Sales Analytics and Data Visualization

Posted by admin on Apr 13, 2026 in Mathematics | 0 comments

Predictive Analytics on Product Sales Data

This section demonstrates how to perform predictive analytics on product sales data using Python libraries such as Pandas, NumPy, and Scikit-learn.

import pandas as pd
import numpy as np
import matplotlib.pyplot as plt

from sklearn.model_selection import train_test_split
from sklearn.linear_model import LinearRegression
from sklearn.metrics import mean_squared_error, r2_score

# Sample product sales data
data = {
    'Month': pd.date_range(start='2022-01-

Essential Concepts in Economics, Budgeting, and Statistics

Posted by admin on Apr 11, 2026 in Mathematics | 0 comments

Zero-Based Budgeting

Zero-based budgeting is a method in which all expenses must be justified for each new period. The budget starts at a zero base, and every function within the organization is analyzed for its needs and costs. Therefore, budgets are built based on what is required for the upcoming period, regardless of the previous budget size.

Taxes

Taxes are a compulsory contribution to state revenue. It is mandatory to pay taxes, which are levied by the government on workers’ income and business

Essential Geometry Theorems and Properties

Posted by admin on Mar 15, 2026 in Mathematics | 0 comments

Quadrilaterals

The sum of the interior angles of a quadrilateral is 360°.
Properties of a parallelogram:
- Opposite sides are equal.
- Opposite angles are equal.
- Consecutive angles are supplementary (sum = 180°).
- Diagonals bisect each other.
- A diagonal divides it into two congruent triangles.
Conditions for a parallelogram:
- Both pairs of opposite sides are equal.
- Both pairs of opposite angles are equal.
- Diagonals bisect each other.
- One pair of opposite sides is equal and parallel.
Mid-Point Theorem: The line segment

Solving Polynomial Equations: Descartes and Cardan Methods

Posted by admin on Mar 12, 2026 in Mathematics | 0 comments

1. Nature of Roots: Descartes’s Rule of Signs

Find the nature of the roots for the equation: x⁴ + 2x² + 3x – 2 = 0

Applying Descartes’ Rule of Signs

Given the function: f(x) = x⁴ + 2x² + 3x – 2

Signs of coefficients: +, +, +, –

Count sign changes:

+ to + (No change)
+ to + (No change)
+ to – (1 change)

Therefore, there is exactly one positive real root.

Replace x with -x:

f(-x) = (-x)⁴ + 2(-x)² + 3(-x) – 2 = x⁴ + 2x² – 3x – 2

Signs: +, +, -, –

Count sign changes:

+ to + (No change)
+ to – (1 change)

Refractive Index Determination: Glass Slab and Prism Experiments

Posted by admin on Mar 11, 2026 in Mathematics | 0 comments

Experiment 6: Refractive Index Determination

Part 1: Refractive Index of a Glass Slab (Pin Method)

Aim

To determine the refractive index of a glass slab material using the pin method.

Apparatus and Materials

Glass slab, drawing board, drawing pins, hairpins, paper, scale, and protractor.

Theory

The refractive index, n, of glass with respect to air is defined by Snell’s Law:

n = sin i / sin r

where i is the angle of incidence and r is the angle of refraction.

A graph plotted with sin r along the X-axis and

Essential Excel Formulas and Functions Reference